1. Field of the Invention
This invention relates generally to automated methods of attitude determination and particularly to methods employing antenna arrays detecting radio waves.
2. Background
Pairs of antennas capable of sensing radio source carrier wave phases may be used to measure the attitude of an object. If the locations of the radio sources are known along with the number of cycles between antenna pairs, then detection of multiple radio sources reveals the attitude of an antenna array through ordinary geometry. An example of a device capable of producing radio source carrier waves is a satellite.
Because the number and location of GPS satellites is known, they are well-adapted for use in making attitude determinations in the out-of-doors. However one is ordinarily only able to sense the instantaneous phase angle of the radio source carrier wave. Thus for an antenna pair, with each antenna reporting a detected phase, there is an ambiguous number of cycles between the antennas. The ambiguity must be resolved in order for attitude to be determined from the radio sources.
The geometry of the antenna configuration limits the scope of the ambiguity in practice. However, the desire for long antenna baselines to achieve accurate attitude measurements results in the integer ambiguity associated with such baselines being computationally impractical to resolve through the evaluation of every candidate integer set. Unremovable noise in carrier phase measurements further complicates integer ambiguity resolution.
Establishing an acceptable integer ambiguity resolution system is vital to the usability of any GPS attitude instrument, however. Correct integer ambiguity resolution is most vital at the initial startup of the instrument, because before any attitude solutions can be calculated, the integers must be determined for at least a minimum set of satellites and antenna pairs.
There are two ways in which integer ambiguity resolution can fail. The first is that no set of integers which meets the criteria for acceptance is found. This type of failure is not disastrous since it is possible to try again with another epoch of data.
The second type of failure is wholly unacceptable, and that is when a set of integers is selected which meets the acceptance criteria, but which is in fact an incorrect set. Such false integer sets would lead to attitude determinations that would be in error, and if undetected, could result in the reporting of hazardously misleading information to the user.
Thus it is critical that above all else, no false set of integers ever be allowed to be used in calculating GPS attitude that is subsequently passed on to the user of the instrument.
In order to facilitate the discussion of integer search reliability, it is useful to define several measures of the quality of the results obtained. The first measure is the pass rate, or the percentage of measurement sets for which an integer set is determined that passes all quality checks and is subsequently used to produce an attitude solution. The second measure is the true initialization rate, defined as the percentage of solutions that both pass and are correct. The final measure is the false initialization rate, defined as the percentage of passing solutions that are incorrect.
It is relatively straightforward, as mentioned previously, to use a combination of quality checks to achieve a high pass rate and high true initialization rate. The very difficult matter is constructing a technique that preserves high pass rates and true initialization rates while suppressing false initializations entirely, or reducing the false initialization rate to zero.
A related approach to integer ambiguity resolution can be presented as an example. There, for a particular antenna array consisting of three antennas and therefore three baselines, a double-difference integer ambiguity resolution scheme was employed that utilized appropriate limits on baseline magnitudes and inter-baseline angles. The candidate integer sets were rank ordered according to the magnitude of the residual vector from the least-squares solution. Extensive efforts were made to select the best possible parametric values for the baseline magnitude and angle limits. As would be expected, the tighter the limits imposed, the lower the pass rates become. However, false initialization rates, while reduced to less than 1%, were never entirely eliminated by this approach.
The answer as to why such an approach cannot completely eliminate false solutions is that in some particular situations of satellite - baseline geometry, so long as there is noise present in the carrier phase measurements, an incorrect set of integers will appear by all measures to represent a superior solution to the correct set of integers. This unfortunate circumstance is generally true whenever there is any integer ambiguity; a false initialization rate of zero cannot be guaranteed through the use of rank ordering and enforcement of solution quality criteria alone.
There are at least two general classes of approaches to addressing this dilemma.
The first approach involves the use of multiple epochs of data to determine the correct integer set. While it might be impossible to identify a false set of integers as false and select the true integer set given a single epoch of data, it will eventually become clear that the true set is superior to the false set as more epochs of data are gathered, particularly as the satellite geometries and/or baseline orientations change.
A second method that can be used to aid the resolution of ambiguity is a priori knowledge of attitude. In fact, if the initial attitude is known precisely, then the integers can be directly calculated for each baseline and no integer ambiguity exists. This method can be useful if there are auxiliary sensors that can be used to initialize the GPS attitude, or after reacquisition of GPS signals following an outage during which attitude has been updated using inertial sensors. However, since a priori knowledge of attitude will never be exact and since there will always be noise in carrier phase measurements, this approach by itself cannot be guaranteed to work flawlessly.
Therefore a method and apparatus for reliable inter-antenna baseline determination is needed.